The Value of the Four Values

In his well-known paper \How computer should think" ((Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Speciically, we provide several theorems that show that the most useful bilattice-valued logics can actually be characterized as four-valued inference relations. In addition, we compare the use of three-valued logics with the use of four-valued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter.